New characterizations of discrete classical orthogonal polynomials

Abstract

We prove that if both {P-n(x)}(n=0)(infinity) and {del(r)P(n)(x)}(n=r)(infinity) are orthogonal polynomials for any fixed integer r greater than or equal to 1, then {P-n(x)}(n=0)(infinity) must be discrete classical orthogonal polynomials. This result is a discrete version of the classical Hahn's theorem stating that if both {P-n(x)}(n=0)(infinity) and {(d/dx)P-r(n)(x)}(n=r)(infinity) are orthogonal polynomials, then {P-n(x)}(n=0)(infinity) are classical orthogonal polynomials. We also obtain several other characterizations of discrete classical orthogonal polynomials. (C) 1997 Academic Press.